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INTRO LOGIC

This is the schedule for Unit 1 of the Logic Translations and Sentential Logic course. The exam will cover 10 arguments worth 4 points each (40% of the exam) and 12 translations worth 5 points each (60% of the exam). The exam will test your understanding of standard and non-standard connectives in sentential logic.

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INTRO LOGIC

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  1. INTRO LOGIC TRANSLATIONS IN SENTENTIAL LOGIC2 DAY 06

  2. Schedule for Unit 1 40% of Exam 10 arguments 4 pts each 60% of Exam 12 translations5 pts each

  3. Standard Connectives(have special symbols) and & or  not  if–then 

  4. Non-Standard Connectives(must be paraphrased) …xor… neither-nor if-otherwise …if… unless-in-which-case only if necessary if and only if sufficient unless

  5. Non-Standard Connectives – 1 • xor • or, butnotboth and • (  ) &( & ) •  • ( & ) (  & ) exclusive ‘or’

  6. Non-Standard Connectives – 2 neither-nor neithernor notandnot &   (  )

  7. Non-Standard Connectives – 3 • if • ifthen •  …if…

  8. Non-Standard Connectives – 4 only if onlyif notifnot ifnot then not   

  9. Non-Standard Connectives – 5 if and only if  if and onlyif  if and onlyif (  ) & (    )

  10. Non-Standard Connectives – 6 unless  unless   if not   if not  if not  then    

  11. …if…otherwise… • I will play tennis • if it is sunny; • otherwise, • I will play racketball T if S ;otherwise, R this answers two questions: what will I do if it's sunny? what will I do otherwise(i.e., if it is notsunny)? play tennis play racketball

  12. if – otherwise (cont.) ifit’s sunny, then I’ll play tennis furthermore if it’s not sunny, then I’ll play racketball if S then T and ifnot S then R ( S  T ) & ( S  R )

  13. …unless…in which case… • I will play tennis unless it rains, • in which case I will play squash T unless R, in which case S this answers two questions: what will I do unless it rains (i.e., if it does not rain)? what will I do in case it rains (i.e., if it doesrain)? play tennis play squash

  14. unless-in-which-case (cont.) ifit doesnot rain, then I’ll play tennis furthermore if it does rain, then I’ll play squash ifR then T and if R then S ( R  T ) & ( R  S )

  15. Necessary Conditions in order that I get an A it is necessary that I take 4 exams in order for me to get an A it is necessary for me to take 4 exams in order to get an A it is necessary to take 4 exams taking 4 exams is necessary for getting an A

  16. Necessary Conditions (cont) • simplest paraphrase: • is necessary for This amounts to saying if does not happen, thenneither does  ifnot thennot 

  17. Example taking 4 exams E is necessary forgetting an AA ifE does not happen, thenneither does A ifnot EthennotA EA

  18. Sufficient Conditions in order that I get an A it is sufficient that I get a hundred in order for me to get an A it is sufficient for me to get a hundred in order to get an A it is sufficient to get a hundred getting a hundred is sufficient for getting an A

  19. Sufficient Conditions (cont) • simplest paraphrase: • is sufficient for This amounts to saying ifdoes happen, thensodoes ifthen 

  20. Example getting a hundred H is sufficient forgetting an AA ifHdoes happen, thensodoesA ifHthenA HA

  21. Negations Of Necessity getting a hundred His notnecessary for getting an A A not ( H is nec for A ) ifnot H then not A  ( H  A ) it is not true that ifyou don’tget a hundred then you won’tget an A

  22. Negations of Sufficiency taking all the exams Eis notsufficient forgetting an A A not ( E is suf for A ) if E then A  ( E  A ) it is not true that ifyou (merely) take all the exams then you will get an A

  23. Basic Statements •  is necessary for  •  is sufficient for  •  is notnecessary for  •  is notsufficient for 

  24. Combinations •  is bothnecessaryandsufficient for  •  is necessary, butnotsufficient, for  •  is sufficient, butnotnecessary, for  •  is neithernecessarynorsufficient for 

  25. Example 1 • averaging (at least) fifty A • is bothnecessaryandsufficient for • passing P A is necessary for P ( A P ) and & A is sufficient for P ( A  P )

  26. Example 2 • taking four exams E • is necessarybutnotsufficient for • getting an A A E is necessary for A ( E A ) but & E is not sufficient for A ( E  A )

  27. Example 3 • getting a hundred H • is sufficientbutnotnecessaryfor • getting an A A H is sufficient for A ( H  A ) but & E is not necessary for A ( H A )

  28. Example 4 • attending class A • is neithernecessarynorsufficient for • passing P A is not necessary for P ( A P ) and & A is notsufficient for P ( A  P )

  29. THE END

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